Final answer:
To find the area under the standard normal curve that lies to the left of the z-score of -1.66, subtract the area to the left of -1.66 from the area to the left of 1.5.
Step-by-step explanation:
To find the area under the standard normal curve that lies to the left of the z-score of -1.66, we can use the Z-table. The Z-table provides us with the area to the left of each z-score. From the given information, we know that the area to the left of a z-score of -0.40 is 0.3446 and the area to the left of a z-score of 1.5 is 0.9332. To find the area between these two z-scores, we subtract the smaller area from the larger area: 0.9332 - 0.3446 = 0.5886. Therefore, the area under the standard normal curve that lies to the left of the z-score of -1.66 is approximately 0.5886.